Final answer:
To make the vegan version of the brownie recipe, (1)/(3) cup of applesauce is needed.
Step-by-step explanation:
To make the vegan version of the brownie recipe, half of the oil needs to be replaced with an equal amount of applesauce. The original recipe requires (2)/(3) cup of oil, so half of that would be (2)/(3) ÷ 2 = (1)/(3) cup of oil. Therefore, (1)/(3) cup of applesauce is needed to make the vegan recipe.